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NeuroQuantology | June 2014 | Volume 12 | Issue 2 | Page 170-179
Beauvais F., Intersubjective agreement in a quantum-like model
Intersubjective Agreement in a
Quantum-like Model of “Paradoxical”
Experiments in Biology
Francis Beauvais
ABSTRACT
In previous articles, we proposed to describe the results of Benveniste’s experiments using a theoretical framework
based on quantum logic. This formalism described all characteristics of these controversial experiments and no
paradox persisted. This interpretation supposed to abandon an explanation based on a classical local causality such as
the “memory of water hypothesis. In the present article, we describe with the same formalism the cognitive states of
different experimenters who interact together. In this quantum-like model, the correlations observed in Benveniste’s
experiments appear to be the consequence of the intersubjective agreement of the experimenters.
Key Words: : quantum-like probabilities, quantum cognition, scientific controversy, Benveniste’s experiments
DOI Number: 10.14704/nq.2014.12.2.737
NeuroQuantology 2014; 2:170-179
An unresolved scientific controversy1
The expression “memory of water” refers to the
hypothesis that specific biological information
could be “imprinted” in water samples in the
absence of the biologically active molecules that
served as “template”. This hypothesis became
famous in 1988 when the journal Nature
published an article from Benveniste’s team and
other scientists reporting that high dilutions of
antibodies apparently kept biological activity
when added to white blood cells called
basophils despite no molecule from the initial
solution could possibly be present (Davenas et
al., 1988). The story of water memory and the
Corresponding author: Francis Beauvais, MD, PhD.
Address: MD, PhD. 91, Grande Rue, 92310 Sèvres, France
Phone: + 33 1 45 34 92 20
Fax: 33 1 79 72 31 60
e-mail  [email protected]
Relevant conflicts of interest/financial disclosures: The authors
declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a
potential conflict of interest.
Received: 10 February 2014; Revised: 14 April 2014;
Accepted: 2 May 2014
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arguments exchanged by Benveniste and
Maddox, the director of Nature, have been
described elsewhere (de Pracontal, 1990;
Alfonsi, 1992; Schiff, 1998; Benveniste, 2005;
Beauvais, 2007). This episode belongs now to
the history of sciences and, for many scientists,
the “memory-of-water” story ended when
Nature concluded that these experiments were
a delusion (Benveniste, 1988; Maddox, 1988a;
b; Maddox et al., 1988).
To be exact, Benveniste’s team was not
the first to report such results. Indeed, the idea
that high dilutions of pharmacological
compounds could have biological effects is one
of the pillars of homeopathy (Walach et al.,
2005). As a matter of fact, the early
experiments in Benveniste’s laboratory were
performed in the context of scientific contracts
with homeopathy firms (Davenas et al., 1987;
Poitevin et al., 1988). Less known are the
devices and biological systems that Benveniste’s
team set up after 1988 until his death in 2004.
These innovative devices were most probably
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Beauvais F., Intersubjective agreement in a quantum-like model
related to the determination of Benveniste for
standing out from homeopathy and putting the
debate on scientific grounds. Two models
emerged from this period and very promising
results, which were regularly communicated to
scientific congresses, were obtained (Hadji et
al., 1991; Benveniste et al., 1992; Aïssa et al.,
1993; Benveniste et al., 1994; Aïssa et al., 1995;
Benveniste et al., 1996; Benveniste et al., 1997;
Benveniste et al., 1998; 1999). The first model
was the isolated rodent heart model (using
Langendorff device) and the other one was the
in vitro coagulation model, which was
thereafter completely automated. The two
biological models and the results that were
obtained have been described in details
elsewhere (Beauvais, 2007).
The methods for “imprinting” information
in water were also “improved” during this
period and Benveniste’s team built up different
electronic devices that allowed “transferring
molecular information” from one vial
containing target molecule to another vial
containing
“uninformed”
water.
The
“imprinted” water sample was tested on a
biological system. For the first attempts, the
electronic transfer was performed using two
electric coils (one for input and the other for
output) wired at a low-frequency electronic
amplifier (Aïssa et al., 1993; Benveniste et al.,
1994; Aïssa et al., 1995). Then Benveniste’s
team showed that the “information” captured
by the electric coil at input could be recorded on
the hard disk of a computed via its sound card
and then “replayed” to water samples placed in
the electric coil at output (Benveniste et al.,
1996; Benveniste et al., 1997; Benveniste et al.,
1998). The term “digital biology” was coined by
Benveniste to describe these new experiments.
As previously described, very impressive and
clear-cut experiments were obtained (Beauvais,
2007). However, if these experiments were so
spectacular, why Benveniste did not convince
other scientists of the reality of these
phenomena?
The paradoxes of Benveniste’s
experiments
The simplest answer to the question raised in
the last paragraph is that an unexpected and
puzzling
phenomenon
poisoned
the
experiments, more particularly some blind
experiments performed with the participation
of other scientists (Beauvais, 2008). We have
described in details these experiments and a
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comprehensive analysis of one of them has been
recently published (Beauvais, 2013c).
In order to easily describe this issue, a
biological effect not different than background
noise (no significant change of the biological
parameter) will be symbolized with “↓” and
biological signal (significant change of the
biological parameter) with “↑”. Suppose that the
expected results were ↓↓↓↓↑↑↑↑ (i.e. 4 “inactive”
samples and 4 “active” samples in this order).
When open-label experiments were performed,
expected results were obtained, namely:
↓↓↓↓↑↑↑↑. This was also the case for in-house
experiments blinded by an observer that we call
a “type-2 controller” (Figure 1). These results
were therefore in favor of Benveniste’s claims.
The concerns mainly occurred during “public
demonstrations”. Indeed, when Benveniste’s
team considered that the devices and the
biological model were mature, gave the
expected results and were free of external
disturbances, a meeting with other scientists
was set up in order to provide a definite proof of
concept on the reality of the biological effects
related to “memory of water” and “digital
biology”. For these blind experiments with the
participation of observers that we call “type-1
controllers” (Figure 1), something like that was
obtained: ↓↑↑↓↓↑↓↑, i.e. a signal was observed at
the expected places not better than random.
Nevertheless, the important point is that we
should expect: ↓↓↓↓↓↓↓↓, i.e. only background
noise and no signal.
The fact that a signal (↑) was observed –
whatever its place – was nevertheless a
fascinating result (Beauvais, 2012). Initially, the
apparent mismatches between “inactive” and
“active” samples in these experiments were
interpreted by Benveniste as errors during
handling of samples. Then, it appeared that
such trivial explanation was false and “jumps”
of activity from one tube to another were
thought to be due to electromagnetic crosscontamination of samples. Note that a series of
samples prepared and treated in the same
conditions but not blinded by a type-1 controller
gave “expected” results. Therefore, the
explanation
by
“electromagnetic
contamination” was limited. It was as if the
conditions of blinding (type-1 vs. type-2
controllers) influenced the outcomes (Beauvais,
2008; Beauvais, 2013c). In a next section, we
will precisely define the role of the different
observers who participated to the blinding of
the experiments.
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Beauvais F., Intersubjective agreement in a quantum-like model
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The unexplained emergence of a “signal”
from background noise (in other words, a
biological parameter significantly changed) was
the main reason why Benveniste’s considered
that these experiments merited to be continued.
Contamination whatsoever (from water or from
the electromagnetic environment) were then
called to the rescue to explain a posteriori these
mismatches. As a consequence, after each
failure
of
a
“public
demonstration”,
Benveniste’s team engaged in a headlong rush
to improve electronic devices and biological
models. The quest of the crucial experiment
became the main objective.
present, but they concluded that they had been
unable to reproduce these results after the
departure of the team (Jonas et al., 2006).
According to the authors of the article,
experimenter’s effects could explain these
results of Benveniste’s experiments, but they
concluded that a theoretical framework was
necessary before continuing this research.
Figure 1. Type-1 and type-2 controllers. In Benveniste’s blind
experiments, success or failure depended on the conditions of
blinding. Therefore, we defined two types of controllers whose
role was to supervise and to check the results. These observers
replaced the initial label of all the experimental samples by a
code number. The type-2 controller was inside the laboratory
where he/she could interact with the experimenter and the
experimental system. As a consequence, the type-2 controller
was always in the same “reduced” state as both the
experimenter and the experimental device. In contrast, the
type-1 controller was outside the laboratory and he/she did not
interact with the experimenter or experimental device and had
no information on the on-going measurements. When all the
samples had been tested, the results of the experiments for
each sample (no effect or significant effect) were sent to the
type-1 controller. The controllers (type-1 or type-2) assessed
the rate of concordant pairs by comparing the two lists for each
sample: state of the biological model (no change, “↓” or
significant change, “↑”) and corresponding label under code
number (“inactive” or “active” sample).
Quantum-like correlations of the
“cognitive states” of the experimenter
To solve the dilemma described in the previous
section, we proposed in a series of articles to
describe these experiments using notions from
quantum logic (Beauvais, 2012; 2013a;
Beauvais, 2013c; b). In the model that we
described, there is no need of postulating
“memory of water”. Taking into account the
experimental
context
allows
describing
“success” and “failure” as two facets of the same
phenomenon. The paradoxes described in the
above section are therefore dissolved in this
model. The use of quantum logic is reasonable
since classical probabilities are only a special
case of quantum probabilities and, at worst,
calculations would show that classical
probabilities are sufficient to describe these
experiments.
These efforts culminated in 2001 when a
team commissioned by the United States
Defense Advanced Research Projects Agency
(DARPA) investigated a robot analyzer
designed by Benveniste’s team to automatically
perform “digital biology” experiments with the
coagulation model. In an article published in
2006, the team of investigators reported that
some effects supporting “digital biology” had
been observed when Benveniste’s team was
In quantum logic, the term “observable”
refers to a physical variable. To each observable
corresponds a set of possible “pure states”.
Before any measurement/observation, the
quantum system is in a “superposed” state of all
possible pure states. The states are represented
in a Hilbert space (i.e., a vector space with a
finite or infinite number of dimensions and
with a complex or real inner product). Note
that the superposed state is not a simple
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Therefore we face a dilemma: we can
consider that “memory of water” (and its
avatars) exists or does not exist; but, in both
cases, we are uncomfortable. We can deem that
“memory of water” exists because biological
signal emerged from background noise and
because there were numerous coherent results,
particularly in some blind experiments. On the
contrary, we can judge that “memory of water”
does not exist because this hypothesis is not
compatible with our knowledge of physics of
water, because reproduction of
these
experiments by other teams was generally not
convincing or because blind experiments during
“public demonstrations” were not better than
random.
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Beauvais F., Intersubjective agreement in a quantum-like model
mixture of the pure states; indeed, the unique
pure state selected randomly by the
measurement is undetermined before the
measurement (there are no hidden variables
that determine the outcome).
We define the “cognitive state” A of an
experimenter/observer as the information on
all possible measures/observations (with their
respective probabilities) performed by this
experimenter/observer
on
this
system.
Mathematically, A is represented by a vector
 A in a Hilbert vector space. In Figure 2, the
state vector of the cognitive state A is the
superposition of the two pure states A-1 and A+1,
which are the tw  A  a A1  b A1 o possible
outcomes of a measurement: with |a|2 + |b|2
= 1.
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many authors have proposed to describe
cognitive
mechanisms
and
information
processing in human brain by using notions and
tools initially developed for quantum
mechanics. These new quantum-like tools
allowed addressing problems in human
memory,
decision
making,
personality
psychology, etc, which were paradoxical in a
classical frame (see for example the special
issue of Journal of Mathematical Psychology in
2009) (Bruza et al., 2009; Busemeyer et al.,
2012)
The norm a of the vector obtained after
projection of  A on the axis of the pure state
A+1, is assimilated to a probability amplitude;
therefore, the probability for the cognitive state
to be associated with A+1 is |a|2.
In our model of Benveniste’s experiments,
the first set of observables is the cognitive state
A associated with expected results, in other
words the “labels” of the samples: i.e. A
associated with sample designated as “inactive”
(AIN) or A associated with samples designated
as active (AAC); all experimental samples are
physically equivalent, only their “labels” differ.
The numbers of inactive and active samples are
defined for a series of experiments. For
example, if the numbers of inactive and active
samples are equal, then P (AIN) = P (AAC) = 0.5.
The second set of observables is the
cognitive state A associated with the
concordance of pairs: the experimenter
observes the outcome with the biological system
(background noise “↓” or signal “↑”) and
compares with the expected result (i.e., the label
of the sample: “inactive” or “active”). The pure
states of the second set of observables are ACP if
pairs are concordant and ADP if pairs are
discordant. Pairs are concordant if “expected”
results fit observed results: i.e., A↓ associated
with AIN and A↑ associated with AAC. Otherwise,
pairs are discordant. Note that the probability
associated with A↑ must be different of zero even
though this probability can be low (signal must
be present in background noise).
The use of quantum logic outside
quantum physics has been already described;
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Figure 2. Superposition of quantum states. In quantum logic, a
quantum system is a “superposed” state of all possible pure
states. The states are represented in a Hilbert space (i.e., a
vector space). In this formalism, the cognitive state A is
symbolized by ΨA. The probability associated with the pure
state A+1 is the square of the probability amplitude a (which is
the norm of the projection vector of the vector ΨA).
In our previous articles (Beauvais, 2013a;
b; c), we showed that the paradoxes of
Benveniste’s experiments disappeared if the
possible “cognitive states” of the experimenter
were described according to some principles
from quantum physics (superposition and
probability
interferences).
We
obtained
equations that correctly described the
characteristics of Benveniste’s experiments,
namely emergence of signal from background
noise, disturbance of blind experiments (type 1
vs. type 2) and difficulties for other teams to
reproduce the experiments.
The cognitive state of A was described as:
 A  ( p cos   q sin  ) ACP  ( q cos  p sin  ) ADP
(Eq. 1)
where p and q are the rates of “inactive” and
“active” labels, respectively; θ is the angle of the
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Beauvais F., Intersubjective agreement in a quantum-like model
rotation matrix for change of basis (from
AIN/AAC basis to ACP/ADP basis).
According to Eq. 1, the probability to
observe concordant pairs is:
Prob quant ( ACP )  ( p cos   q sin  ) 2
This probability is maximal (equal to 1)
if sin   q .
Why pairs were concordant remained
however unexplained. Technically speaking, the
couple of observables AIN/AAC and ACP/ADP
behaved as noncommuting observables. In this
article, we address this issue by considering
what happens if several experimenters – not
only one – perform experiments.
Bob make experiments in their respective
laboratories with two experimental devices.
They observe the rates of concordant and
discordant pairs for the same series of samples
(labeled “inactive” or “active”).
According to the quantum logic, we can
describe the two cognitive states A and B of
Alice and Bob. Eq. 1 described in previous
section is simplified with a  p cos  q sin 
and b  q cos   p sin  :
 A  a ACP  b ADP
(Eq. 1)
 B  c BCP  d BDP
(Eq. 2)
Note that the probability amplitudes a, b, c and
d are real number (not complex numbers) in
our quantum-like model. The cognitive states of
the experimenters can be jointly described by a
unique state vector that is the tensor product of
 A and  B :
 A   B  ac ACP BCP  ad ACP BDP
bc ADP BCP  bd ADP BDP
(Eq. 3)
A and B are now described in a new
Hilbert subspace defined by the four orthogonal
bases ACP BCP , ACP BDP , ADP BCP
and
ADP BDP . Eq. 3 shows that Alice and Bob
observe the same results with a probability (ac)2
for concordant pairs and with a probability
(bd)2 for discordant pairs. The outcomes of
their respective experiments are different
(concordant for one, discordant for the other)
with a probability (ad)2 + (bc)2.
These results are trivial, but this
presentation allows defining the formalism of a
joint description of two experimenters before
introducing the next section.
Figure 3. Experiments with two experimenters. The pictures
describe (A) two experimenters doing Benveniste’s experiments
in two separate places and (B) two experimenters doing joint
experiments. Due to the intersubjective agreement, the state
vectors that describe the cognitive states of the experimenters
in these two experimental situations are different (see text).
Two experimenters doing experiments in
two separate places
First, we consider a simple situation with
“Benveniste’s experiments” performed in two
separate places by two experimenters: Alice
with cognitive state A and Bob with cognitive
state B (Figure 3A). We suppose that Alice and
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Two experimenters doing the same
experiments
We now suppose that Alice and Bob are doing
the same “Benveniste’s experiments” at the
same place with a unique experimental device
(Figure 3B). The state vector that describes
their cognitive states is the same tensor product
as above:
 A   B  ac ACP BCP  ad ACP BDP
bc ADP BCP  bd ADP BDP
(Eq. 3)
However, there is now a major difference:
we must assume intersubjective agreement of
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Beauvais F., Intersubjective agreement in a quantum-like model
the two experimenters. In other words, Alice
and Bob must agree on the results they observe
together. It is not possible that for one
experiment with a given label (IN or AC), Alice
observes a concordant pair, whereas Bob
observes a discordant pair. After a quantum
toss, Bob could not observe that outcome is tail,
whereas for the same coin Alice observes that
the outcome is head. In Eq. 3, the “branches” of
the state vector with the bases ACP BDP and
do not comply with intersubjective
agreement and therefore we write:
ADP BCP
 AB =
ac

ACP BCP 
bd
With   (ac) 2  (bd )2
must be equal to 1.
(Eq. 4)
ADP BDP

since total probability
Therefore,
due
to
intersubjective
agreement, we have defined an operation (Eq.
4) that joins two cognitive states of
experimenters observing the same experiments.
We can easily calculate that there is a unique
state vector  B that is a neutral element for
any state vector  A for this operation:
B 
1
2
BCP 
1
2
BDP
A  B =
a
ACP  b ADP
  
1
 2
BCP 
1

BDP 
2

→  AB  a ACP BCP  b ADP BDP
In other words, if the cognitive state of
Bob is “neutral” (as defined above), the
probability for concordant pairs observed by
Alice and Bob together or observed by Alice in
the absence of Bob are the same.
We also easily see that  B  BCP and
 B  BDP are two absorbent elements for any
state of A. Thus, if  B  BCP (i.e., c = 1, d = 0,
Δ = a):
 AB =
ac

ACP BCP 
bd

ADP BDP = ACP BCP
In other words, if the cognitive state of
any experimenter is associated with only
concordant pairs, then both experimenters
observe only concordant pairs (conversely, if all
pairs are discordant for one experimenter, then
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both experimenters observe only discordant
pairs).
Intersubjective agreement as the source
of concordant outcomes
Eq. 4, which is the consequence of
intersubjective agreement, has important
consequences. Thus, suppose that Alice
observes concordant pairs with probability 0.51
when she performs the experiments alone and
suppose that Bob observes concordant pairs
with probability 0.52 when he performs the
experiments alone:
Pquant (ACP) = 0.51
Pquant (BCP) = 0.52
According to Eq. 4, when Alice and Bob
perform joint experiments, the probability that
they both observe concordant pairs is:
Pquant (ABCP) = (0.51× 0.52) / (0.51 × 0.52 +
0.49 × 0.48) = 0.53.
Therefore, the probability to observe
concordant pairs changed for both Alice and
Bob, simply by interacting and doing joint
experiments.
In real physical world, a measurement is
submitted to microscopic random fluctuations.
Thus, when light is reflected or transmitted
through a beam splitter, each state is associated
with a certain probability amplitude, a or b;
these variables are characteristic of the beam
splitter for a given adjustment. Since the beam
splitter is not an isolated object, it is submitted
to many influences of the environment.
Therefore, the ratio of probabilities for the
reflected and transmitted light is submitted to
tiny variations around a2/b2 due to thermal or
mechanical noise.
In our model of Benveniste’s experiments,
we hypothesize that, for similar reasons,
random microscopic fluctuations lead to
random changes of probability amplitudes. At a
given time t, Eq. 1 is modified with ε, a positive
or negative real number << 1:
 A  a 2   ACP  b2   ADP
We model this situation by beginning with
the initial cognitive states A and B as neutral
states:
A 
1
2
ACP 
1
2
ADP
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Beauvais F., Intersubjective agreement in a quantum-like model
B 
1
2
BCP 
1
2
BDP
The random microscopic fluctuations
associated with A and B are independent (the
portions of environment around Alice and Bob
are different) (Figure 3B). We define ε1 and ε2
as infinitesimal random changes (positive or
negative)
of
Pquant (ACP)
and Pquant (BCP),
respectively:
Pquant (ACP) = 0.5
at
Pquant (ACP) = 0.5 + ε1 at
microscopic fluctuation;
t=0
and
first random
Pquant (BCP) = 0.5
at
Pquant (BCP) = 0.5 + ε2 at
microscopic fluctuation.
t=0
and
first random
The intersubjective agreement must be
guaranteed and the common probability is
calculated using Eq. 4. The common probability
for A and B is now 0.5 + ε. For the next random
microscopic fluctuation, we define ε3 and ε4 as
infinitesimal random changes (positive or
negative)
of
Pquant (ACP)
and Pquant (BCP),
respectively:
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If many teams of two, three or more
experimenters perform the experiments, the
overall mean of probability for concordant
pairs remains equal to 0.5, but two
populations appear: experimenters X with
Pquant (XCP) = 1 and experimenters Y with
Pquant (YCP) = 0. In other words, the random
outcomes of concordant pairs and discordant
pairs are distributed in two populations of
experimenters: those who “turn down” and
those who “turn up” as depicted in Figure 4.
However, for symmetry reasons, nothing in the
formalism allows choosing one of the two
solutions for a given team of experimenters.
With a single observer, there is no
significant change of the probability of
concordant pairs; for each sample that is
observed by a “neutral” experimenter, the
probabilities to be associated with concordant
or discordant pairs are equal and each reduced
state is obtained randomly (Figure 4). Indeed,
with a single experimenter, the intersubjective
agreement
has
no
consequence
(the
experimenter is always in agreement with
him/herself).
Pquant (ACP) = (0.5 + ε) + ε3
Pquant (BCP) = (0.5 + ε) + ε4
The same calculation is repeated several
times by reinjecting at each step the updated
common probability of A and B. In Figure 4, the
evolution of Pquant (ACP) is shown after several
calculation steps with a very small random
variation of Pquant (ACP) at each step ([-0.5; 0.5]
× 10-15). We see that a divergence occurs after
several iterations with two possible outcomes:
all pairs are concordant with Pquant (ACP) = 1 or
all pairs are discordant with Pquant (ACP) = 0.
Therefore, the probability amplitudes
associated with each state of A (or B, C, etc)
dramatically change during joint observations
with other experimenters
A 
1
2
ACP 
1
2
ADP → 1 ACP  0  ADP
or
A 
1
2
ACP 
1
2
ADP → 0  ACP  1 ADP
Eq. 4 can be easily adapted for three or
more experimenters and the divergence occurs
after a lower number of iterations when the
number of experimenters increases (Figure 4).
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Figure 4. Divergence from “neutral” to “absorbent” states with
a number of experimenters ≥ 2. Small changes in the
probability of concordant pairs (related to microscopic random
fluctuations) have crucial consequences if the number of
experimenters who do the same experiment is ≥ 2. The
elementary change of probability of concordant pairs is very
small in this simulation: from –0.5 to +0.5 × 10-15 (the smallest
change allowed in Excel sheet). In this computer simulation,
probabilities diverge after several iterations toward one of the
two “absorbent” states: either “all pairs are concordant” or “all
pairs are discordant”. Of importance, for a single experimenter,
the probability of concordant pairs remains close to 0.5.
Note that even if we take into account
random microscopic fluctuations, the means of
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Beauvais F., Intersubjective agreement in a quantum-like model
the probabilities for concordant pairs do not
change in the experimental situation described
in Section 4 (two experimenters doing
experiments in two separated places).
Therefore, the intersubjective agreement
appears to be necessary for the appearance of
concordant outcomes.
How asymmetry was introduced in
Benveniste’s experiments?
We have now a hypothesis on the origin of the
relationship between labels of samples and
concordance of pairs. A strong constraint
emerges as clearly depicted in Figure 4 if we
take into account both the intersubjective
agreement
and
random
microscopic
fluctuations. Nevertheless, for symmetry
reasons, nothing in the formalism favors one
relationship over the other one (“all
concordant” vs. “all discordant”). Therefore,
asymmetry must be added from outside into the
formalism.
In Section 1, we have briefly summarized
the successive Benveniste’s experiments and we
reported that mainly three biological models
were routinely used that led to a bulk of
coherent results (basophil leukocytes, isolated
rodent heart and in vitro coagulation). In fact,
these models have been progressively selected
among many others that were at disposal of
Benveniste’s team in laboratory, either already
in routine or specially developed for the
purposes of this research. All these potential
models were systematically assessed and
abandoned if no clear “effect” of high dilutions
or “digital biology” could be evidenced. Only the
models that evidenced not only signal, but also
correct link of signal with “active” samples were
selected. To put it simply, only experimental
models with results that fitted the upper part of
Figure 4 were selected.
The preservation of asymmetry among the
experimenters/observers is suggested by the
formalism. We have seen that there are two
“absorbent” elements. Therefore, there is a
possibility of “contagion” from one “absorbent”
experimenter (with high rates of “success”) to
any experimenter, for example a “neutral
experimenter”. Such a “mechanism” could
maintain high rates of successful experiments
in a circle of collaborating experimenters (this
is exactly the definition of a scientific team).
In summary, biological models with their
dedicated experimenter(s) that concur to
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achieve “expected” results have a selective
advantage and they are more willingly
reproduced; these experimental correlations
(“successful experiments”) are maintained
through “absorbent” states in the circle of the
collaborating experimenters.
Blind experiments with a type-2
controller
When a type-2 controller participates to blind
experiments, he/she assesses the concordance
of pairs in conditions strictly comparable with
the experimental situation described above
(Section 5) with two experimenters (see details
on type-2 controller in legend of Figure 1).
Therefore, a type-2 controller is equivalent to a
“neutral” experimenter with cognitive state B:
B 
1
2
BCP 
1
2
BDP
With or without blinding by type-2
controller, the probability of concordant pairs
associated with A does not change. By
definition, a type-2 controller is “neutral”.
Blind experiments with a type-1
controller
First demonstration
When a blind experiment is performed with the
participation of a type-1 controller, the rate of
concordant pairs is assessed by this observer
(see details on type-1 controller in the legend of
Figure 1). This change in conditions of blinding
has important consequences in the context of a
quantum-like model.
This experimental situation is formally
comparable to a “which-path” measurement in
the
two-slit
experiment
and classical
probabilities apply. Indeed, the type-1
controller assesses the rate of concordant pairs
with knowledge of the label of each pair. It
could be argued that a type-2 controller has also
knowledge of the labels, but he/she is on the
same “branch” than the experimenter (they
both observe the same “reduced” states of
experimental device and labels). In contrast, a
type-1 controller – who is “outside” – breaks the
superposition of the states of A because the
information on the label must be taken into
account to calculate the rate of concordant pairs
associated with A:
Pclass ( ACP )  P( AIN )  P ( ACP |AIN )  P ( AAC )  P ( ACP |AAC )
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NeuroQuantology | June 2014 | Volume 12 | Issue 2 | Page 170-179
Beauvais F., Intersubjective agreement in a quantum-like model
We define p = P(AIN) as the proportion of
inactive labels and q = P(AAC) as the proportion
of active labels:
Pclass ( ACP )  p  P ( ACP |AIN )  q  P ( ACP |AAC )
At the end of the experiments and before
unblinding, the rate of samples with no effect is
equal to p and the rate of samples associated
with a signal is equal to q (the information on
the values of p and q are available to all
participants, including the experimenter).
Therefore, the probability for an inactive
sample to be associated with a concordant pair
is P(ACP | AIN) = p and the probability for an
active sample to be associated with a
concordant
pair
is
P(ACP | AAC) = q.
Consequently, the overall probability to observe
concordant pairs is:
Pclass ( ACP )  p 2  q 2 .
Second demonstration
There is another possible description of the
experimental situation with a type-1 controller.
For each sample, the “success” or “failure”
(concordant or discordant pairs) is known with
certainty by the type-1 controller; there is no
superposition but a mixture of two states: BCP
or BDP . The cognitive states A and B
associated with each sample (inactive label with
a probability equal to p and active labels with a
probability equal to q), are described by taking
into account the intersubjective agreement:
 AB  (a ACP  b ADP )  BCP → ACP BCP
or
 AB  (a ACP  b ADP )  BDP → ADP BDP
The state ACP BCP is observed with a
probability equal to p for inactive labels and
with a probability equal to q for active labels.
Overall, the probability to observe concordant
pairs is p2 for inactive labels and q2 for active
labels:
Pclass ( ACP )  p 2  q 2 .
Comparison of Pclass and Pquant for
concordant pairs
We can now compare Pquant (APC) and Pclass (APC).
If all pairs are concordant in the superposed
state,
then
Pquant (APC)
=
1
and
Pclass (APC) = p2 + q2.
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Pquant ( ACP )  Pclass ( ACP )  1  p2  q 2  2 pq
The term 2pq is typical of quantum or
quantum-like interferences; it disappears when
a Type-1 controller breaks the superposition of
the possible states of A:
Pquant (APC) = (p + q)2
↓
Type-2 controller
Pquant (APC) = (p + q)2
↓
Type-1 controller
Pclass (APC) = p2 + q2
“Jumps” of “biological activities”
between samples
It is important to note that even in an
experiment checked by a type-1 controller, a
signal is observed with some samples. Suppose,
for example, that – in the absence of type-1
controller – an experimenter routinely observes
a signal with 100% of “active” samples and with
0% of “inactive” samples (with p = q = 0.5). If
the experiments are checked by a type-1
controller, the rates of signal associated with
“active” samples decrease from 100% to 50%
(because (p + q)2 = 1 and p2 + q2 = 0.5);
consequently, the rates of signal associated with
“inactive” samples increase from 0% to 50%.
Therefore, in the context of classical logic, these
results could be interpreted as “jumps” of the
alleged biological activity from “active” to
“inactive” samples.
Conclusions
The apparent “jumps” of biological activity
between samples were a disconcerting
phenomenon, which was most probably the
main reason why Benveniste failed to convince
his peers at demonstrating the concepts of
“memory of water” or digital biology. In our
model, this phenomenon is a logical
consequence of the formalism and no ad hoc
hypotheses are introduced. Only quantum logic
allows building a simple model taking into
account both the emergence of a signal from
background noise and the differences in
outcomes for blinding with type-1 vs. type-2
controllers. This formalism does not predict the
outcomes of individual events, but describes
how these events are connected. Therefore,
these experiments cannot be used to send
useful information and there is no causal
relationship between events observed together.
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NeuroQuantology | June 2014 | Volume 12 | Issue 2 | Page 170-179
Beauvais F., Intersubjective agreement in a quantum-like model
In the present article, we consider the
interaction of the cognitive states of several
experimenters using the same quantum-like
logic. We see that a strong constraint emerges
from the formalism due to the intersubjective
agreement. The observables are then engaged in
quantum-like correlations.
Some
questions
remain
however
unanswered. One of the most important issues
is to define the limits of the phenomena
observed by Benveniste’s team and described by
the equations of the quantum-like formalism.
Could comparable results be seen by replacing
the biological systems used in Benveniste’s
References
Aïssa J, Jurgens P, Litime MH, Béhar I and Benveniste J.
Electronic transmission of the cholinergic signal. Faseb J
1995; 9: A683.
Aïssa J, Litime MH, Attias E, Allal A and Benveniste J.
Transfer of molecular signals via electronic circuitry.
Faseb J 1993; 7: A602.
Alfonsi M. Au nom de la science, Bernard Barrault, Paris.
1992.
Beauvais F. L’Âme des Molécules – Une histoire de la
"mémoire de l’eau". Collection Mille Mondes (ISBN: 9781-4116-6875-1); 2007. available at http://www.millemondes.fr
Beauvais F. Memory of water and blinding. Homeopathy
2008; 97: 41-42.
Beauvais F. Emergence of a signal from background noise in
the "memory of water" experiments: how to explain it?
Explore (NY) 2012; 8: 185-196.
Beauvais F. Description of Benveniste’s experiments using
quantum-like probabilities. J Sci Explor 2013a; 27: 43-71.
Beauvais F. “Memory of water” without water: the logic of
disputed experiments. Axiomathes 2013b; 1-16.
Beauvais F. Quantum-like Interferences of Experimenter's
Mental States: Application to “Paradoxical” Results in
Physiology. NeuroQuantology 2013c; 11: 197-208.
Benveniste J. Benveniste on the Benveniste affair. Nature
1988; 335: 759.
Benveniste J. Ma vérité sur la mémoire de l'eau, Albin Michel,
Paris, 2005.
Benveniste J, Aïssa J and Guillonnet D. Digital biology:
specificity of the digitized molecular signal. Faseb J 1998;
12: A412.
Benveniste J, Aïssa J and Guillonnet D. The molecular signal
is not functional in the absence of "informed" water. Faseb
J 1999; 13: A163.
Benveniste J, Aïssa J, Litime MH, Tsangaris G and Thomas Y.
Transfer of the molecular signal by electronic
amplification. Faseb J 1994; 8: A398.
Benveniste J, Arnoux B and Hadji L. Highly dilute antigen
increases coronary flow of isolated heart from immunized
guinea-pigs. Faseb J 1992; 6: A1610.
Benveniste J, Jurgens P and Aïssa J. Digital
recording/transmission of the cholinergic signal. Faseb J
1996; 10: A1479.
eISSN 1303-5150
179
experiments by any classic or quantum random
generator? Could anybody play the role of a
“Benveniste’s experimenter”?
In conclusion, we proposed in previous
articles that Benveniste’s experiments could be
described as the consequence of quantum-like
interferences of the possible cognitive states of
the experimenters. However, the source of the
concordant outcomes remained unknown. In
the present article, we propose that the
quantum-like concordance of outcomes is the
consequence of the intersubjective agreement of
the experimenters.
Benveniste J, Jurgens P, Hsueh W and Aïssa J. Transatlantic
transfer of digitized antigen signal by telephone link. J
Allergy Clin Immunol 1997; 99: S175.
Bruza P, Busemeyer JR and Gabora L. Introduction to the
special issue on quantum cognition. J Math Psychol 2009;
53: 303-305.
Busemeyer JR and Bruza PD. Quantum models of cognition
and decision, Cambridge University Press. 2012.
Davenas E, Beauvais F, Amara J, Oberbaum M, Robinzon B,
Miadonna A, Tedeschi A, Pomeranz B, Fortner P, Belon P,
Sainte-Laudy J, Poitevin B and Benveniste J. Human
basophil degranulation triggered by very dilute antiserum
against IgE. Nature 1988; 333: 816-818.
Davenas E, Poitevin B and Benveniste J. Effect of mouse
peritoneal macrophages of orally administered very high
dilutions of silica. Eur J Pharmacol 1987; 135: 313-319.
De Pracontal M. Les mystères de la mémoire de l'eau, La
Découverte, Paris. 1990.
Hadji L, Arnoux B and Benveniste J. Effect of dilute histamine
on coronary flow of guinea-pig isolated heart. Inhibition
by a magnetic field. Faseb J 1991; 5: A1583.
Jonas WB, Ives JA, Rollwagen F, Denman DW, Hintz K,
Hammer M, Crawford C and Henry K. Can specific
biological signals be digitized? Faseb J 2006; 20: 23-28.
Maddox J. Waves caused by extreme dilution. Nature 1988a;
335: 760-763.
Maddox J. When to believe the unbelievable. Nature 1988b;
333: 787.
Maddox J, Randi J and Stewart WW. "High-dilution"
experiments a delusion. Nature 1988; 334: 287-291.
Poitevin B, Davenas E and Benveniste J. In vitro
immunological degranulation of human basophils is
modulated by lung histamine and Apis mellifica. Br J Clin
Pharmacol 1988; 25: 439-444.
Schiff M. The Memory of Water: Homoeopathy and the Battle
of Ideas in the New Science, Thorsons Publishers, London.
1998.
Walach H, Jonas WB, Ives J, Van Wijk R and Weingartner O.
Research on homeopathy: state of the art. J Altern
Complement Med 2005; 11: 813-829.
www.neuroquantology.com